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{"id":25129,"date":"2023-04-17T19:11:16","date_gmt":"2023-04-17T18:11:16","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25129"},"modified":"2023-04-27T00:40:11","modified_gmt":"2023-04-26T23:40:11","slug":"duas-retas-e-dois-referenciais-cartesianos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25129","title":{"rendered":"Duas retas e dois referenciais cartesianos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25129' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25129' class='GTTabs_curr'><a  id=\"25129_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25129' ><a  id=\"25129_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_25129'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Observa as retas <em>r<\/em> e <em>s<\/em> representadas nos referenciais da figura.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25132\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25132\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\" data-orig-size=\"543,328\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag173-T4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\" class=\"aligncenter wp-image-25132\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4-300x181.png\" alt=\"\" width=\"420\" height=\"254\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4-300x181.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png 543w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<ol>\n<li>Quais s\u00e3o as coordenadas dos pontos A, B, C e D pertencentes \u00e0 reta <em>r<\/em>?<br \/>O que t\u00eam em comum?<\/li>\n<li>Escreve uma equa\u00e7\u00e3o da reta <em>r<\/em>.<\/li>\n<li>Indica as coordenadas dos pontos E e F pertencentes \u00e0 reta <em>s<\/em>.<\/li>\n<li>Indica o valor de<br \/>\\[\\frac{{ordenada\\,do\\,ponto\\,F &#8211; ordenada\\,do\\,ponto\\,E}}{{abcissa\\,do\\,ponto\\,F &#8211; abcissa\\,do\\,ponto\\,E}}\\]<\/li>\n<li>Escreve uma equa\u00e7\u00e3o da reta <em>s<\/em>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25129' onClick='GTTabs_show(1,25129)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25129'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Observa as retas <em>r<\/em> e <em>s<\/em> representadas nos referenciais da figura.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25132\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25132\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\" data-orig-size=\"543,328\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag173-T4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png\" class=\"aligncenter wp-image-25132\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4-300x181.png\" alt=\"\" width=\"420\" height=\"254\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4-300x181.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4.png 543w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li>As coordenadas dos pontos A, B, C e D s\u00e3o as seguintes: \\(A\\left( {3,5} \\right)\\), \\(B\\left( {3,2} \\right)\\), \\(C\\left( {3,0} \\right)\\)\u00a0e \\(D\\left( {3, &#8211; 3} \\right)\\).<br \/>Os pontos t\u00eam a mesma abcissa.<br \/><br \/><\/li>\n<li>Uma equa\u00e7\u00e3o da reta <em>r<\/em>: \\(x = 3\\).<br \/><br \/><\/li>\n<li>As coordenadas dos pontos E e F s\u00e3o as seguintes: \\(E\\left( { &#8211; 2, &#8211; 1} \\right)\\) e \\(F\\left( {0,3} \\right)\\).<br \/><br \/><\/li>\n<li>C\u00e1lculo do valor da express\u00e3o dada:<br \/>\\[\\frac{{ordenada\\,do\\,ponto\\,F &#8211; ordenada\\,do\\,ponto\\,E}}{{abcissa\\,do\\,ponto\\,F &#8211; abcissa\\,do\\,ponto\\,E}} = \\frac{{3 &#8211; \\left( { &#8211; 1} \\right)}}{{0 &#8211; \\left( { &#8211; 2} \\right)}} = \\frac{4}{2} = 2\\]<\/li>\n<li>Ora, o declive da reta r \u00e9 \\({a_r} = \\frac{{3 &#8211; \\left( { &#8211; 1} \\right)}}{{0 &#8211; \\left( { &#8211; 2} \\right)}} = \\frac{4}{2} = 2\\) e a ordenada na origem \u00e9 \\({b_r} = 3\\) (ordenada do ponto B).<br \/>Assim, \\(y = 2x + 3\\) \u00e9 uma equa\u00e7\u00e3o da reta <em>s<\/em>.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25129' onClick='GTTabs_show(0,25129)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa as retas r e s representadas nos referenciais da figura. Quais s\u00e3o as coordenadas dos pontos A, B, C e D pertencentes \u00e0 reta r?O que t\u00eam em comum? Escreve&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25133,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,345,344],"series":[],"class_list":["post-25129","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-graficos-de-funcoes-afins","tag-8-o-ano","tag-funcao-afim","tag-grafico"],"views":73,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag173-T4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25129","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25129"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25129\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25133"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25129"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}